The angle of repose is the maximum angle at which a stack of granular material or an object on a slope will remain stable. It is used in engineering and science to analyze slopes, design machinery, and predict behavior of natural phenomena. The angle is affected by the size, shape, and moisture content of the material. Various methods are used to calculate it.
Angle of repose is a term used in science and engineering and can have two related meanings. It is generally used to describe the maximum angle, measured upwards from the horizontal, at which a stack of a particular granular material will remain stable without any of the material sliding downwards. It can also refer to a combination of a ramp or other slope and an object resting on it. In this case, it is the maximum angle at which the ramp or slope will support the object without sliding down. In either case, the critical angle of repose, as it is more properly known, will always be greater than 0° and less than 90°, and most materials will have one of 45° or less.
Any material of a granular nature, even when the individual units are very large, such as pieces of crushed concrete or rock the size of a stone, naturally form a cone-shaped pile when deposited onto a flat surface from above. The natural profile of this cone will approximate the angle of repose for that particular material or blend. Very small or smooth grains that exert little friction on each other will tend to form mounds with shallower sides. Coarser grains or grains that adhere strongly to each other tend to form mounds with steeper sides and a higher angle. Moisture content also significantly affects this measurement for most materials.
Geologists, as well as mining and civil engineers, often use this measurement to analyze slopes and levees for collapse danger, as well as to help assess potential avalanche danger. It is useful in the design of machinery for storing and transporting granular materials as it can provide an engineer with information on the appropriate size and shape of such devices. Civil engineers use data when designing and managing construction and land management projects, such as levees, dams, and roadbeds. Geologists and volcanologists use it to predict the possible behavior of cinder cones and sand volcanoes, as well as to study the processes associated with rock erosion and sediment deposition.
Engineers and scientists use a number of methods to calculate the angle of repose of a granular substance or mixture. Calculations and formulas employing previously published data are one method, and there are several simple experiments to determine the angle for any substance with grains small enough to be easily handled. Depending on the method and accuracy of possible measurements, the figures tend to be close approximations rather than exact values, but this does not reduce or eliminate their usefulness.
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